"Neither?"

Molina was stunned. [with _ dream]ā

After settling down, she looked at Lu Zhou and said in a suspicious tone, "I know you are a genius...... Although the Goldbach conjecture is not my field of study, if I heard me correctly, you are not planning to overturn this century-old work, are you? ”

Lu Zhou smiled faintly and said in a relaxed tone.

"The problem of a+b boils down to a complex formulation of Goldbach's conjecture, that every large even number N can be expressed as A+B, where the number of prime factors of A and B does not exceed a and b, respectively. When a=b=1, the problem will eventually return to the original formulation, i.e., any even number greater than 2 can be written as the sum of two prime numbers. ”

The number of prime factors is 1, which is naturally a prime number.

Therefore, the form of 1+1 is still the Goldbach conjecture itself.

Molina said in a mocking tone, "You mean that for a century, the people who studied Goldbach's conjecture have been doing useless work?" ”

"Of course not," Lu Zhou shook her head, and suddenly threw out a question that she didn't expect, "Do you know anything about sports?" ”

Mo Lina was slightly stunned, frowned, and said, "Sports? ”

Lu Zhou: "You know about the long jump." ”

Molina pursed her lips and said speechlessly, "Of course." ”

Lu Zhou smiled faintly and said, "The A+B proof method opened by Brown is equivalent to a run before the long jump." While the run-up time itself does not count towards the score, is the run-up useless? In the same way, A+B is the equivalent of Goldbach's conjecture. If it weren't for it, there would be no later Great Sieve Method, an inspiring and potential tool for analytic number theory research. It can even be said that the value of the large sieve method has surpassed the Goldbach conjecture itself. ”

Regardless of whether the sieve method can really cross the last 1+1, it has fulfilled its historical mission and plays an important role in analytic number theory.

Including Lu Zhou, they have benefited a lot from it.

Brushing the long hair from her ears, Molina looked at Lu Zhou: "So, how are you going to prove it?" ”

The corners of Lu Zhou's mouth hooked up a confident smile.

"Of course, it's your own way to prove it."

Not sure why.

Seeing the confident smile on his face, Molina's heartbeat inexplicably accelerated for two seconds.

Of course, for a woman who has decided to marry math, the so-called heartbeat is only a moment......

……

The solution of a mathematical conjecture requires the accumulation of work and a creative genius.

Both are indispensable.

It's like Fermat's theorem.

When Taniyama Shimura's conjecture was proven, even though people could not yet see the concrete prospects, everyone knew it in their hearts, because a tool that could solve the problem had emerged. Sure enough, Andrew Wiles, finally, completed this historic work.

But for Goldbach's conjecture, whether it is the large sieve method or the circle method, it is almost like this.

The work of predecessors has done a lot of foreshadowing, but whether it is Chen's theorem from "9+9" to "1+2", or Helfgot's proof of Goldbach's weak conjecture under odd number conditions, there is only one last step away. Even the significance of Chen's theorem is more for other mathematicians to understand that the road of the big sieve method has been achieved by Chen Jingrun, and this road is no longer possible.

It's the same with the circle method.

It is precisely for the same reason that in his speech at the end of last year, Wolfgort used "We still have a long way to go to fully prove the Goldbach conjecture" as the final remark, expressing his hope that the Bach conjecture will not be solved in the short term.

At the very least, there is no hope for the circle method.

Lu Zhou couldn't help but start to reflect on whether these two methods had reached a dead end.

When he first worked on the twin prime conjecture, he faced a similar problem.

Zhang Yitang's research cleverly selected the lambda function to limit the spacing of prime pairs to 70 million, and his successor narrowed this number to 246 within a year, and then could not go any further.

Lu Zhou's initial idea was to choose an appropriate lambda function, but after countless attempts, he finally found that this path did not work.

There were so many lambda functions to choose from, but no matter how much he searched, he couldn't find the right one.

It was not until he tried a completely different way of proving in a state of inspiration and introduced the theory of topology into the concept of sieve that the door to a new world was opened.

Although this idea was first mentioned in Professor Zelberg's 95 paper on the Goldbach conjecture, it was he who improved it and introduced it into the prime pair problem.

Later, Lu Zhou introduced the knowledge of group theory on this basis, pushed the pair of prime numbers with a finite distance to infinity, and solved the Polygnac conjecture on this basis.

Therefore, Lu Zhou engraved a new name for this weapon of his own, that is, "group construction method".

But when thinking about Goldbach's conjecture, habitual thinking makes him selectively ignore his tools.

On the surface, the group construction method seems to have nothing to do with the Goldbach conjecture, but at its root it evolved from the sieve method and has always been there to solve the prime number problem.

As long as it is improved, it is not necessary that this tool cannot be used in the Goldbach conjecture, which is also a prime number problem.

When this mathematical method is constantly perfected, refined enough to solve many problems, and perfected to the point of changing from a toothpick to a Swiss army knife, its meaning may no longer be a simple tool, but gradually evolve into a theoretical framework! And it's a theoretical framework in analytic number theory!

Just like Shinichi Mochizuki, a well-known "middle two disease" in mathematics, created the "intercosmic Teihmüller theory" and the "extraterrestrial arithmetic pure structure" when he was studying the AB conjecture.

There are precedents to follow, whether it is to establish a theory first and then prove its value, or to develop a novel theory while studying a specific mathematical problem.

From Goldbach's conjecture, Lu Zhou vaguely saw hope.

……

After coming out of the eating club, Lu Zhou did not go to the library for a while after eating as usual, but went to the Institute for Advanced Study in Princeton.

Although he did not make an appointment, according to Professor Delin's own account, he would be here every night from 6 to 8 p.m.

Knocking on the office door, Lu Zhou walked in.

Stopping the ballpoint pen in his hand, Professor Deligne looked at Lu Zhou, who was standing across from his desk, and asked in a relaxed tone.

"You've thought about it?"

Lu Zhou nodded and said.

"Yes, I intend to continue my research...... I'm sorry, but I may not be able to spare the energy to join your project. ”

Deligne nodded, not resentful.

Sitting in his position, it is difficult to be as narrow-minded as the boss of an ordinary doctoral student, and use some boring tests to test whether the student is "obedient". As he said at the beginning, he offered Lu Zhou two options.

Deligne: "I respect your choice, but as your mentor, I need to know what your research topic is?" ”

Lu Zhou replied truthfully: "Goldbach conjecture." ”

Deligne nodded, not as surprised as Molina was at the subject he was studying, and the usual calmness on his face surprised Lu Zhou, who threw out this proposition.

Don't......

The old Déligne also thinks that he is the "best person" to solve this conjecture?

How embarrassing is that.

Lu Zhou felt a little proud in his heart.

Deligne: "The Goldbach conjecture is an interesting question, I studied it when I was younger, but I didn't go into it and probably won't be able to help you much. At present, the closest research results in the world are Chen's theorem and Helfgot's proof of weak conjecture, and I am looking forward to you working on something new based on it. ”

"Of course, in addition to your own research, there are also some non-research work that I need you to do. For example, teaching assistants and the like. ”

Lu Zhou nodded: "No problem...... If it's a course in number theory or functional analysis, I can still talk about it. ”

"The main thing is analytic number theory, and I believe that with your ability, it is more than enough for this job...... In addition, I have prepared a welcome gift for you. ”

After a pause, old Mr. Deligne reached out and pulled open the drawer, took out a certificate-like thing from it, and placed it on the table, a smile softened on his serious face.

"I've heard from you that your family is not in good condition. Yesterday, when I helped you go through the admission procedures, I helped you solve the problem of financial aid by the way, and you can take this thing to the teaching office in a while, and by the way, the tuition fee matter was also solved. ”